Basic algebra formulas that you can revise anytime and anywhere

FORMULAS FOR BEGINNER (a+b) ^2= a^2+b^2+2ab (a+b) ^2= (a-b) ^2+4ab (a-b) ^2= a^2+b^2-2ab (a-b) ^2= (a+b) ^2-4ab a^2+b^2= (a+b) ^2-2ab a^2+b^2= (a-b) ^2+ 2ab a^2-b^2= (a+b) (a-b) (a+b+c) ^2= a^2+b^2+c^2+2(ab+bc+ac) (a-b-c) ^2= a^2+b^2+c^2-2(ab-bc+ac) (a+b) ^3= a^3+b^3+3ab(a+b) (a-b) ^3= a^3-b^3+3ab(a-b) a^3+b^3= (a+b) (a^2-ab+b^2) a^3-b^3= (a-b) (a^2+ab+b^2) a^4-b^4= (a^2-b^2) (a^2+b^2) = (a^2+b^2) (a+b) (a-b) a^5+b^5= (a+b) (a^4-a^3b+a^2b^2-ab^3+b^4) a^5-b^5= (a-b) (a^4+a^3b+a^2b^2+ab^3+b^4)

Things You Probably Didn't Know About Loses In Optical Fibre

There is some types of losses in Optical fibre..

What is Attenuation?

Attenuation is the loss of light energy as the light pulse travels from one end of the cable to the other end.
  • It is called as signal loss or fibre loss.
  • It also decides the number of repeaters required between transmitter and receiver.
  • Attention is directly proportional to the length of cable.
α= 10 log10(Pi/Po) [in db/Km]
where,
Pi = Input power
Po= Output power
α= Attenuation constant
The various losses are:
  • Absorption loss
  • Scattering loss
  • Dispersion loss
  • Bending loss

Absorption loss:

Absorption of light energy due to heat of ion impurities results in dimming of light at the end of fibre.

1. Intrinsic absorption :
It is caused by the interaction with one or more components of glass.
  • It occurs when photon interacts with an electron in the valance band and excites it to a higher energy level.

2. Extrinsic Absorption :

It is also called impurity absorption.
  • Results from the presence of transition metal ions like iron L, cobalt and from OH ions that is from water.
Scattering loss:

It occurs due to microscopic variations in the material density and manufacturing defects..

1. Linear Scattering :
  • Rayleigh Scattering loss
  • Mie Scattering loss
  • Waveguide Scattering loss
Rayleigh Scattering :
Unequal distribution of molecular densities causes this type of scattering.
Mie Scattering :
This scattering causes during fibre fabrication. It causes the light to scatter outside the fibre.
Waveguide Scattering :
It is a result of variation in the core diameter, imperfections of the core cladding interface change in RI of either core of cladding.

2. Non linear Scattering :
  • Stimulated Scattering
Dispersion loss:
An optical signal travels along the fibre it becomes increasingly distorted.
1. Intermodal Dispersion :
Pulse broadening due to intermodal dispersion results from the propagation delay differences between modes within multimode fibre.
2. Intramodal Dispersion :
It is a pulse spreading that occurs with in a single mode.
3. Material Dispersion
4. Waveguide Dispersion


Bending Loss:

The loss which exists when an optical fibre undergoes bending is called bending losses.
There are two types of bending :

1. Macroscopic bending:
Bending in which complete fibre undergoes bends which causes certain modes not to be reflected and therefore causes loss to the cladding.
2. Microscopic bending:
Either the core or cladding undergoes slight bends at its surface. It causes light to be reflected at angles when there is no further reflection.

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